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Fractional powers and singular perturbations of differential operators

TitleFractional powers and singular perturbations of differential operators
Publication TypePreprint
2018
AuthorsMichelangeli, A, Ottolini, A, Scandone, R
Document NumberSISSA;01/2018/MATE
InstitutionSISSA

We develop the construction of the fractional powers of singular
(point-like) perturbations of the Laplacian, and the construction of singular
perturbations of fractional powers of the Laplacian, and we compare such two
constructions focusing on their perturbative structure for resolvents and on the
local singularity structure of their domains. In application to the linear and
non-linear Schr odinger equations for the corresponding operators we outline a
programme of relevant questions that deserve being investigated.

http://preprints.sissa.it/handle/1963/35305

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